Deep learning techniques have been successfully applied in handwriting recognition. Oracle bone inscriptions (OBI) are the earliest hieroglyphs in China and valuable resources for studying the etymology of Chinese characters. OBI are of important historical and cultural value in China; thus, textual research surrounding the characters of OBI is a huge challenge for archaeologists. In this work, we built a dataset named OBI-100, which contains 100 classes of oracle bone inscriptions collected from two OBI dictionaries. The dataset includes more than 128,000 character samples related to the natural environment, humans, animals, plants, etc. In addition, we propose improved models based on three typical deep convolutional network structures to recognize the OBI-100 dataset. By modifying the parameters, adjusting the network structures, and adopting optimization strategies, we demonstrate experimentally that these models perform fairly well in OBI recognition. For the 100-category OBI classification task, the optimal model achieves an accuracy of 99.5%, which shows competitive performance compared with other state-of-the-art approaches. We hope that this work can provide a valuable tool for character recognition of OBI.

This paper presents a novel approach to safety verification based on neural barrier certificates synthesis for continuous dynamical systems. We construct the synthesis framework as an inductive loop between a Learner and a Verifier based on barrier certificate learning and counterexample guidance. Compared with the counterexample-guided verification method based on the SMT solver, we design and learn neural barrier functions with special structure, and use the special form to convert the counterexample generation into a polynomial optimization problem for obtaining the optimal counterexample. In the verification phase, the task of identifying the real barrier certificate can be tackled by solving the Linear Matrix Inequalities (LMI) feasibility problem, which is efficient and makes the proposed method formally sound. The experimental results demonstrate that our approach is more effective and practical than the traditional SOS-based barrier certificates synthesis and the state-of-the-art neural barrier certificates learning approach.

In this paper, we propose a safe reinforcement learning approach to synthesize deep neural network (DNN) controllers for nonlinear systems subject to safety constraints. The proposed approach employs an iterative scheme where alearnerand averifierinteract to synthesize safe DNN controllers. Thelearnertrains a DNN controller via deep reinforcement learning, and theverifiercertifies the learned controller through computing a maximal safe initial region and its corresponding barrier certificate, based on polynomial abstraction and bilinear matrix inequalities solving. Compared with the existing verification-in-the-loop synthesis methods, our iterative framework is a sequential synthesis scheme of controllers and barrier certificates, which can learn safe controllers with adaptive barrier certificates rather than user-defined ones. We implement the tool SRLBC and evaluate its performance over a set of benchmark examples. The experimental results demonstrate that our approach efficiently synthesizes safe DNN controllers even for a nonlinear system with dimension up to 12.